Besides the muon, recent results concerning the anomalous magnetic moment of the electron might also be interpreted as NP hints [1]}. On the one hand, perturbative calculations of \(a_e=\frac{g_e-2}{2}\) , which have reached impressive levels [2]}, [3]}, [4]}, [5]}, [6]}, yield \(a_e^{\rm SM}\)  as a series in powers of the fine structure constant \(\alpha \) . On the other hand, we have precise measurements of \(a_e^{\rm Exp}\)  such as [7]}. In the past, such measurements were indeed used to infer values of \(\alpha \) . On the contrary, measurements of atomic recoils [8]} provide now more precise determinations of \(\alpha \) , which give values of \(a_e^{\rm SM}\)  such that
\(\delta a_e^{\rm Exp,Cs}=-(8.7\pm 3.6)\times 10^{-13}\, ,\) 
